Question

Pls help me answer this

Answer 1

Answer: 30 cm

Step-by-step explanation:

The volume of the composite solid is 17000 cm³. To find h, we must first subtract the volume of the half cylinder from the composite volume.

From the figure, AE = MK, and so the radius of the half cylinder is 10cm. The volume of the half cylinder is thus $\frac{1}{2}$ the volume of a cylinder. The volume of a cylinder is πr²h. So a half cylinder is 1/2 πr²h. This gives us a volume of  $\frac{1}{2} (\frac{22}{7})(10 cm)^2(28 cm) = 4400 cm^3$.

Thus, the volume of the right prism is 17000cm³ - 4400cm³ = 12600cm³. Consider the cross-section ABKJ. If we multiply this by AE, we'll have the volume of the right prism.

The ABKJ is a trapezoid so it's area is $\frac{1}{2}(AJ + BK) \cdot AB$. Thus the volume of the right prism is $\frac{1}{2}(AJ + BK) \cdot AB \cdot AE$. This gives us $\frac{1}{2}(28 + 14) \cdot h \cdot 20 = 12600$, and thus h = 30 cm.